Nonlinearity test for complex time series without surrogates.

Area of Science:

• Dynamical Systems Analysis
• Time Series Analysis
• Nonlinearity Testing

Background:

• Dynamical system linearity is assessed using time series nonlinearity tests.
• The common method of surrogates generates linear time series to test for nonlinearity, but can introduce spurious correlations.
• Existing surrogate techniques often involve frequency domain manipulation, leading to artifacts.

Purpose of the Study:

• To develop a novel nonlinearity test that bypasses the need for surrogate data generation.
• To address the limitation of spurious nonlinearities introduced by conventional surrogate methods.
• To provide a more robust method for distinguishing linear from nonlinear time series.

Main Methods:

• The proposed test utilizes the autocorrelation function of the experimental time series.
• It statistically assesses if observed correlations could originate from a linearly transformed Gaussian time series.
• The method avoids frequency domain manipulations and surrogate data creation.

Main Results:

• The new nonlinearity test demonstrated excellent performance on established linear and nonlinear time series models.
• It successfully distinguished between linear and nonlinear behaviors in tested datasets.
• The method avoids the introduction of artificial nonlinearities inherent in surrogate data.

Conclusions:

• The developed nonlinearity test offers a reliable alternative to surrogate-based methods.
• It effectively identifies the nature of dynamical systems without generating potentially flawed linear surrogates.
• This approach provides a more direct and accurate assessment of time series linearity.